相关论文: All Difference Family Structures arise from Groups
In this paper, six constructions of difference families are presented. These constructions make use of difference sets, almost difference sets and disjoint difference families, and give new point of views of relationships among these…
Difference sets and their generalisations to difference families arise from the study of designs and many other applications. Here we give a brief survey of some of these applications, noting in particular the diverse definitions of…
The circular external difference family and its strong version, which themselves are of independent combinatorial interest, were proposed as variants of the difference family to construct new unconditionally secure non-malleable threshold…
Families of objects appear in several contexts, like algebraic topology, theory of deformations, theoretical physics, etc. An unified coordinate-free algebraic framework for families of geometrical quantities is presented here, which allows…
A linking system of difference sets is a collection of mutually related group difference sets, whose advantageous properties have been used to extend classical constructions of systems of linked symmetric designs. The central problems are…
Given an initial family of sets, we may take unions, intersections and complements of the sets contained in this family in order to form a new collection of sets; our construction process is done recursively until we obtain the last family.…
A difference matrix over a group is a discrete structure that is intimately related to many other combinatorial designs, including mutually orthogonal Latin squares, orthogonal arrays, and transversal designs. Interest in constructing…
Families form the basis of society, and anthropologists have characterised various family systems. This study developed a multi-level evolutionary model of pre-industrial agricultural societies to simulate the evolution of family systems…
We study groups generated by sets of pattern avoiding permutations. In the first part of the paper we prove some general results concerning the structure of such groups. In the second part we carry out a case-by-case analysis of groups…
Necessary and sufficient conditions for finite semihypergroups to be built from groups of the same order are established
\'{E}tale difference algebraic groups are a difference analog of \'{e}tale algebraic groups. Our main result is a Jordan-H\"{o}lder type decomposition theorem for these groups. Roughly speaking, it shows that any \'{e}tale difference…
We construct infinite families of graphs that are determined by their generalized spectrum. This construction is based on new formulae for the determinant of the walk matrix of a graph. The graphs constructed here all satisfy a lower…
The uniform structure on a differential space defined by a family of generators is considered.
It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…
The selection pressures that have shaped the evolution of complex traits in humans remain largely unknown, and in some contexts highly contentious, perhaps above all where they concern mean trait differences among groups. To date, the…
A disjoint $(v,k,k-1)$ difference family in an additive group $G$ is a partition of $G\setminus\{0\}$ into sets of size $k$ whose lists of differences cover, altogether, every non-zero element of $G$ exactly $k-1$ times. The main purpose of…
Difference sets are subsets of a group satisfying certain combinatorial property with respect to the group operation. They can be characterized using an equality in the group ring of the corresponding group. In this paper, we exploit the…
In this note, we provide several constructions of Deza Cayley graphs over groups having a generalized dihedral subgroup. These constructions are based on a usage of (relative) difference sets.
Necessary and sufficient conditions for finite commutative semihypergroups to be built from abelian groups of the same order are established.
The arise of disagreement is an emergent phenomenon that can be observed within a growing social group and, beyond a certain threshold, can lead to group fragmentation. To better understand how disagreement emerges, we introduce an…